The new measures would apply to unvaccinated members of the public, Alexander Schallenberg added.
It follows a meeting on Friday evening between Mr Schallenberg and state-level leaders to discuss their response to rapidly increasing cases.
“The pandemic is not yet in the rear-view mirror,” Mr Schallenberg said. “We are about to stumble into a pandemic of the unvaccinated.”
Austria reported 20,408 new cases of Covid in the latest seven-day period, according to health authorities, bringing the seven-day average to 228.5 cases per 100,000 people. A week earlier, that figure was at 152.5.
Mr Schallenberg also announced that if the number of Covid patients in intensive care units (ICU) reaches 500, or 25 per cent of the country’s total ICU capacity, entry into businesses such as restaurants and hotels will be limited to those who are vaccinated or recovered from the virus.